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Abstract	A coordinate system describing the interior of organs is a powerful tool for a systematic localization of injured tissue. If the same coordinate values are assigned to specific anatomical landmarks, the coordinate system allows integration of data across different medical image modalities. Harmonic mappings have been used to produce parametric coordinate systems over the surface of anatomical shapes, given their flexibility to set values at specific locations through boundary conditions. However, most of the existing implementations in medical imaging restrict to either anatomical surfaces, or the depth coordinate with boundary conditions is given at sites of limited geometric diversity. In this paper we present a method for anatomical volumetric parameterization that extends current harmonic parameterizations to the interior anatomy using information provided by the volume medial surface. We have applied the methodology to define a common reference system for the liver shape and functional anatomy. This reference system sets a solid base for creating anatomical models of the patient’s liver, and allows comparing livers from several patients in a common framework of reference.
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